Method of determining surface flatness



COLL/MA TED LIGHT Jan. 6, 1959 c. T. GODDARD 2,867,149

METHOD OF DETERMINING SURFACE FLATNESS Filed Oct. 5. 1953 LIGHT RAYS /0SURFACE 70 BE MEASURED SOURCE INVENTOP C. 7. GODDARD ATTORNE V Uflliifid rates METHOD OF DETERMINING SURFACE FLATNESS ApplicationGctober 5, 1953, Serial No. 384,144

4 Claims. (Cl. 88-14) This invention relates to methods of determiningsurface flatness and more particularly to such methods applicable to themeasurement of the flatness of coated cathode surfaces.

The pursuit of improved designs of broadband grid control electron tubesfor use in video or I. F. amplifiers has led to closer and closurespacing between cathode and control grid. Circuit degradation ofgain-band product resulting from stray wiring capacitance suggests theuse of relatively large cathode areas for improved performance. As aresult of these two factors there are several tubes now in manufacturein which the ratio of cathode length to grid-cathode spacing isapproximately 300:1. in tubes now under development the ratio is 700:1.

If it is desired to hold a production quality range of the order of i20percent in important electrical characteristics, it is found that theaverage spacing between control grid and cathode must be held toapproximately ilO percent. In attaining this average spacing range, itis found that the order of an additional percent in tilt, sag, wavinessor twist in the cathode or grid plane is permissible. The ratio ofcathode length to permissible departure from surface flatness is thus7,000z1. This is roughly equivalent to requiring that a football fieldbe graded flat to within one-half an inch. For an electron tube cathodethe problem is more severe since the flatness requirement must be heldfor thousands of hours of operation at the order of 1000 degrees Kelvin.

It is therefore desirable in the manufacture of tubes to be able tomeasure this degree of surface flatness. Measurement by optical flats isnot feasible because of the granular texture of the carbonate coatedsurface. Measurement by conventional mechanical probing of the profilewould damage the carbonate coating and be time consuming for uncoatedcathodes.

It is a general object of this invention to provide a method ofdetermining surface flatness and more particularly to provide such amethod applicable to the measurement of the flatness of coated cathodesurfaces.

More specifically among the objects of this invention are to enable therapid and facile checking of cathodes for surface irregularities priorto their incorporation into vacuum tubes and to enable a quantitativedetermination of the departure of a surface from a priorly chosen plane.

In accordance with one specific embodiment of this invention, a gratingof fine wires or ruled lines is positioned at an angle to the surfacebeing measured and a source of parallel rays of light positioned so asto project the light through the grating at any angle to the surface.Because of the angles of the light and of the grating with respect tothe surface, the distance between successive shadows of the gratingwires or lines on the surface is different from the apparent distancebetween the Wires of the grating themselves when viewed from directlyabove the surface. This gives rise to alternate bands of dark and lightregions, as explained further below.

If the surface is perfectly flat these bands will be atent O straight.If the surface is stepped, the bands will appear to have discontinuitiesin them and themselves appear stepped. If the surface has depressions init, the bands will be bowed. The dark bands will in effect provide alinearly magnified picture of the cross section of the surface beingmeasured.

If the angle between the grating and the surface is small and the lightis incident on the surface at 45 degrees, the deviation or distortion ofthe dark bands from being straight bands, expressed as a ratio, timesthe distance between adjacent wires or lines on the grating is thequantitative amount of the distortion or departure from flatness of thecathode surface. This departure may be a depression, caused during themanufacture of the cathode which has to be observed to prevent theincorporation of this cathode into a tube having close spacing betweencathode and grid, or this departure may be due to a coating on thecathode, the technique of this invention thus giving a quantitativedetermination of coating thickness.

The determination of the ratio of dark band distortion to the distancebetween dark band centers may be made by adjusting the angle of thegrating to the surface to any convenient small value, by using measuringrulers or guides, or by employing a grating having a varying spacing oflines or wires and through which the observation of the pattern is made.

It is therefore a feature of this invention that a determination ofsurface flatness be made by positioning a grating at an angle to thesurface being tested, projecting parallel rays of light through thegrating onto'the surface so as to be incident to the surface at an acuteangle, and observing the resulting pattern of alternate dark and lightbands from a position directly above the surface.

It is a further feature of this lnvention that the light be incident onthe surface at an angle of 45 degrees and that the grating be at a smallangle to the surface so that the ratio of deviation of a dark band froma straight line to the distance between dark bands times the actualdistance between the wires or lines of the grating is a quantitativedetermination of the deviation of the surface from flatness.

A complete understanding of this invention and of these and variousother desirable features may be gained from consideration of thefollowing detailed description and the accompanying drawing, in which:

Fig. 1 is a diagrammatic representation of the apparatus employed in thepractice of this invention;

Fig. 2 is an idealized illustration of one pattern of alternate bands ofdark and light regions observed during the practice of this invention;

Fig. 3 is an idealized diagrammatic representation of the apparatus ofthis invention utilized in the description in the proof of certaingeometric relationships advantageously employed in the practice of thisinvention; and

Figs. 4 through 7 are actual pictures of various patterns of the darkand light bands observed during the practice of this invention.

Turning now to the drawing, Fig. 1 illustrates the apparatus employed inthis novel method. A grating 10,

which may be a fine wire type of grid or may consist of opaque linesruled on a flat glass sheet, is mounted at an angle 0 with respect tothe test surface 11. A grating having 300 to 1000 lines per inch isconvenient for determining departure from flatness of the order of0.0003 to 0.0001 inch. The incident light, which is presumed from asource sufiiciently distant so that the light rays are parallel,describes an angle 41 with respect to the test surface 11. The directionor line of observation is as shown and is perpendicular to the testsurface 11. This observation may be visual or photographic. Each line ofthe grating 10 will casta distinct shadow on the test-surface 11 and theangular position of the light source will cause the observed distancebetween lines or wires of the grating to be different from the observeddistance between the'shadows cast by these lines ou 'the'test surface.Asthese distances are different there will b'e'regions where the shadowsappear to lie between the lines of the grating "and other regions wherethe shadows will be behind lines of the grating. These regions can beseen in Fig. 2 where both the grating lines and shadows are clearlydescribed. Ignoring, for the moment, the-curvature of the regions, wecandetermine that there'are successive regions 14 in which the gratinglines and the shadows nearly coincide and'other regions 15 in which thelines and shadows are interlaced. The regions 14 will appear light orgray while the regions 15 will appear'dark or black. Actually, as

*se'en'in Figs.'4 through 7, the grating lines and shadows arenotindividually visible, but they havebeen depicted in Fig. 2 for purpose'of explanation.

The reason for the appearances of these two distinct regions and theiremployment in measuring techniques and methods in accordance with myinvention 'can be best understood from a consideration of Fig. 3 whichis an idealized diagram of a grating 10 having 11 wires 18 of which thefirst wire is in contact with the surface 11 being tested. As in Fig. 1,the grating 10 makes'an angle 6 with the test surface 11 and the lightrays are at an angle to the test surface 11. In Fig. 3 there are alsodepicted a collimated light source 16 of parallel light rays-and acamera 17 which may be used to photograph the band patterns such as aredepicted in Figs. 4'through 7.

Each of then wires will cast a shadow 19 on'the fiat surface and weassume that the shadow 19 of the (nl)th wire 18 appears in the line ofobservation to be directly under the nth wire 18. The distance betweenthe wires 18 is a and the distance between the shadows 19 is'b. Becauseof the angle 6 of the light rays the distance b will be greater than aand further because of the angle Oat which the grating is inclined tothe surface 11 the distance a will appear to the line of observation tobe smaller than it actually is.

Let us now solve for the distance d between the nth wire and the surface11 in terms of the various parameters of this geometrical system. As wehave assumed that the shadow 19 of the (nl)th wire 18 is directly underthe nth wire 18, a right triangle is formed having as sides d, na and(n-1)b and in which no cos 6=(n1)b (l) A second right triangle is alsoformed in which d=b tan (2) n is the number of wires 18 untilthe shadowof the (n1')th"wire is approximately directly beneath a wire and inactuality is of the order of magnitude of 20 to 30 'or larger forsuchvalues of the angle 9 so that the above assump'tion is valid. It shouldalso be pointed out that the two assumptions with respect to n and 0 areof opposite Sign and therefore tend to correct each other.

Equation 4 states that the distance of the wire 18 under which theshadow 19 of a preceding wire exists is approximately the-distancebetween the wires 18 of the grating 10. If we turn again to Fig. 2 theoccurrence of the shadow of a prior wire under another wire gives riseto the light regions 14 while the occurrence of the shadow 19 betweenthe wires 18, as seen in the line of observation, gives rise to the darkregions 15.

While the proof of Equation 4 has assumed, as seen in Fig. 3, that thefirst wire 18 be contiguous to the surface 11 and that the shadow underthe nth wire be that of the (nl)th wire, this proof can be generalizedas the shadow under the 211th wire will be from the 2(nl)th wire, etc.,and in each case the distance from the wire to the surface will be anintegral multiple of the spacing a between the wires 18 of the grating10. As the distance between all the light regions 14, or conversely thecenters of the dark regions 15, is now determined in terms of the knownspacing of the wires of the grating 10, the application of this valuableexpression, Equation 4, to surface flatness measurements can be readilyexplained.

Fig. 4 depicts the observed patterns of dark and light regions for aparticular cathode surface especially coated to illustrate certainfacets of this invention. In Fig. 4 the cathode has four uncoated areas21 and three coated areas 22, 23 and 24 the thickness of which coatingsare different. The grating is tilted so as to be closest to thecathode'surface at the left edge of the cathode. At the top edge ofthecathode in the first uncoated region 21 are seen three dark bands 26 andthree light bands 27. The grating employed had 400 lines to the inch sothat the spacing a between adjacent lines was 0.0025 inch.

As can be seen in Fig. 4, the dark bands 26 over coating 22 are not inline with the dark bands 26 at the uncoated portion 21. If we measurefrom the center of one dark band 26 on portion 21 to the center of thesame dark band 26 at coating 22 we find that the distance is abouttwo-tenths the distance between the centers of adjacent dark bands onthe uncoated portion 21. As we know that the distance from the gratingto the surface is an integral multiple of the distance a betweenadjacent wires or lines of the grating, we can calculate that the heightof the coating is two-tenths of the distance between adjacent Wires ofthe grating or 0.0005 inch. Because of the direction of the deviation ofthe regions over the coated portion we know that the deviation is causedby an increase, rather than a decrease, in the surface position.Similarly we can determine that the thicknesses of the coatings '23 and24 are approximately 1 and 2 mils, respectively. If the thickness of thelast coating had been exactly 2.5 mils, the dark regions would have beenaligned with the dark regions on the uncoated portion but, as can beseen in the drawing, there are dark transition lines along the lineseparating the uncoated and coated portions which connect the two partsof the same dark region together and which would advise us of the truestate of facts.

Fig. 4 illustrates the application of this technique to recognizingsteps in otherwise perfectly flat surfaces and to determining the amountof the step. Figs. 2 and 5 illustrate the application of this techniquein determining the presence of slight and gradual cavities in thesurface. As can be seen in Fig. 5 the dark bands 30 tend to bow to theleft in the middle. This indicates a slight depres sion in the cathodesurface, the depression being deepest in the center of the cathode andextending out towards both ends. By measuring the deviation of thecenter of the dark band at the center of the cathode from the positionof the center of the dark band if it had been straight, the actual depthof the depression can be determined. In this case, again employing agrating having 400 wires to the inch, the deviation was four-tenths ofthe total distance so the depression was four-tenths of 0.0025 inch or0.0010 inch.

In the commercial checking of cathode surfaces, the

cathodes are individually observed by a worker who may advantageously beprovided with a ruled gauge or a grating in .which the number of linesper inch varied along the grating. He would then determine the readingon the gauge or this special grating for the point of maximum bowing. Ifit indicated a departure of more than a certain percentage from thedistance between dark bands on a perfectly flat surface, the cathodewould be rejected. Such a procedure can readily be mechanized and may beaccomplished by unskilled workers.

Fig. 6 shows the pattern observed on a cathode having both a depressionextending from its center to the two edges and also wrinkles or slightruts on the surface. Such a cathode would be quickly discarded duringthe checking process purely on a visual observation without anymeasurement of the depth of the depressions. The peculiar appearance ofthe dark bands at the very edges of the cathode indicates that thiscathode had sloping sides which did not drop off very rapidly. It isapparent that by employing this technique one can obtain a very accuratepicture of the appearance of the surface of the cathode. Thus theoutline of the dark bands in Fig. 6 are an indication, greatlymagnified, of the outline of the cathode surface itself. It should beemphasized, however, that while the outline of the dark bands shows thesurface configuration magnified no optical magnification is employed.

Fig. 7 illustrates a perfectly flat cathode surface. This cathode hadbeen ground flat before the application of the cathode coating.

It is to be understood that the above-described arrangements areillustrative of the application of the principles of the invention.Numerous other arrangements may be devised by those skilled in the artwithout departing from the spirit and scope of the invention.

What is claimed is:

1. The method of determining surface flatness com prising positioning agrating having closely spaced parallel lines at an acute angle to thesurface whose flatness is to be determined and directly adjacent thesurface, projecting parallel rays of light through the grating onto thesurface at an acute angle to the surface to form grating line shadows onthe surface, and recording through said grating the pattern ofsuperimposed grating line shadows and grating lines to detect deviationsfrom straightness of said grating line shadows, said deviations fromstraightness corresponding to deviations from flatness of said surface.

2. The method of measuring the thickness of a coating on a flat surfacecomprising positioning a grating having closely spaced lines at a smallacute angle and directly adjacent to the surface having the coatingthereon, projecting parallel rays of light through the grating of anangle of to the surface to the form grating line shadows on saidsurface, viewing through said grating the pattern of alternate dark andlight bands resulting from the superposition of said grating lines andsaid grating line shadows from a point directly above said surface, andregistering the deviation of one said band over the coated portion ofsaid surface from its position over the uncoated portion of said surfacerelative to the distance between similar points on adjacent similarbands, whereby said deviation indicates the thickness of said coating interms of the reference fixed by said distance between bands.

3. A method of measuring departures from surface flatness comprising thesteps of positioning a grating having closely spaced parallel linesdirectly adjacent and at a small acute angle to the surface whoseflatness is to be measured, projecting parallel rays of light throughsaid grating to form grating line shadows on said surface, viewingthrough said grating the pattern of alternate dark and light bandsresulting from the superposition of said grating lines and said gratingline shadows, and registering the deviation from linearity of at leastone of said bands over said surface relative to the distance betweensimilar points on adjacent similar bands, whereby said deviationindicates the departure from flatness of said surface in terms of thereference fixed by said distance between bands.

4. The method of producing a pattern of light and dark bands indicativeof the deviation from flatness of a surface under inspection comprisingpositioning a transparent ruled grating in close proximity to saidsurface and' at a small acute angle thereto, directing a collimatedlight beam at a different acute angle through said grating to projectshadows of said grating rulings upon said surface, and photographing theresulting pattern of superimposed rulings and shadows thereof throughsaid grating, whereby said rulings and shadows appear as a pattern ofbands, the deviations from straightness of which serve as a measure ofthe deviations from flatness of said surface.

References Cited in the file of this patent UNITED STATES PATENTS1,590,532 7 Lenouvel June 29, 1926 1,906,803 Mueller May 2, 19332,247,047 Bishop June 24, 1941 2,253,054 Tuttle et al. Aug. 19, 19412,379,263 Vine June 26, 1945 FOREIGN PATENTS 395,649 Great Britain July20, 1933

